The argument of sectional units are fragile and therefore can only contain a limited number of things, unless you're careful. A way out of your situation - against all common uses - is to keep your list inside the section, but provide an alternative "floating argument". This is provided by the optional argument:

\documentclass{scrartcl}
\begin{document}
\section[My three favourite flowers]{My three favourite flowers are:
\begin{enumerate}
\item Roses
\item Daisies
\item Violets
\end{enumerate}
Now I will tell you stuff about them}
\end{document}
If, however, you're only after the sectional unit font, then you can define that and use it accordingly:

\documentclass{scrartcl}
\makeatletter
\newenvironment{SECTION}
{\sectfont\size@section\noindent\ignorespaces}% \begin{SECTION}
{}% \end{SECTION}
\makeatother
\begin{document}
\begin{SECTION}
My three favourite flowers are:
\begin{enumerate}
\item Roses
\item Daisies
\item Violets
\end{enumerate}
Now I will tell you stuff about them
\end{SECTION}
\end{document}
You could even add the section number to it by perhaps using
\makeatletter
\newenvironment{SECTION}
{\refstepcounter{section}%
\sectfont\size@section\noindent%
\thesection\quad\ignorespaces}% \begin{SECTION}
{}% \end{SECTION}
\makeatother
Of course, this would remove all sectional functionality, but I'm not sure whether this is required in your instance.
To match Steven's stack, you can also use this definition:

\documentclass{scrartcl}
\begin{document}
\tableofcontents
\section{\protect\tabular[t]{@{}l}
My three favourite flowers are: \\
~~1. Roses \\
~~2. Daisies \\
~~3. Violets \\
Now I will tell you stuff about them
\protect\endtabular}
\end{document}
The \protection allows for safer travel of fragile arguments.
\documentclass{...}and ending with\end{document}please? – darthbith Jun 16 '14 at 15:22\sections place their arguments in the Table of Contents (if you use it, and is therefore fragile), and it would just seem odd for a document to contain an enumeration/list in the ToC. Also, the formatting is quite excessive to distinguish it from the rest of the text... – Werner Jun 16 '14 at 15:32Apparently LaTeX did try to put the list in the ToC, which understandably didn't work.
– Josephus Jun 16 '14 at 15:48